Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer's Neutrosophic Recognitions In Special ViewPoints

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Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer's Neutrosophic Recognitions In Special ViewPoints

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Henry Garrett^*

This version is not peer-reviewed

Submitted:

03 January 2023

Posted:

05 January 2023

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Abstract

in this research, new setting is introduced for new SuperHyperNotion, namely, Neutrosophic SuperHyperStable. In this research article, there are some research segments for ``Neutrosophic SuperHyperStable'' about some researches on neutrosophic SuperHyperStable. With researches on the basic properties, the research article starts to make neutrosophic SuperHyperStable theory more understandable. Assume a neutrosophic SuperHyperGraph. Then a ``neutrosophic SuperHyperStable'' $\mathcal{I}_n(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices such that there's no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

Keywords:

Subject: Computer Science and Mathematics - Computer Vision and Graphics

MSC: 05C17; 05C22; 05E45

1. Background

Look at [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21] for some researches.

2. Neutrosophic SuperHyperStable

Assume a neutrosophic SuperHyperGraph. Then a “neutrosophic SuperHyperStable”

I_{n} (N S H G)

for a neutrosophic SuperHyperGraph

N S H G : (V, E)

is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common.

Example 2.1.

Assume the neutrosophic SuperHyperGraphs in the Figure 1, Figure 2, Figure 3, Figure 4, Figure 5, Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17, Figure 18, Figure 19 and Figure 20.

On the Figure 1, the neutrosophic SuperHyperNotion, namely, neutrosophic SuperHyperStable, is up. $E_{1}$ and $E_{3}$ neutrosophic SuperHyperStable are some empty neutrosophic SuperHyperEdges but $E_{2}$ is a loop neutrosophic SuperHyperEdge and $E_{4}$ is an neutrosophic SuperHyperEdge. Thus in the terms of SuperHyperNeighbor, there’s only one neutrosophic SuperHyperEdge, namely, $E_{4} .$ The neutrosophic SuperHyperVertex, $V_{3}$ is isolated means that there’s no neutrosophic SuperHyperEdge has it as an endpoint. Thus neutrosophic SuperHyperVertex, $V_{3},$ is contained in every given neutrosophic SuperHyperStable. All the following neutrosophic SuperHyperSets of neutrosophic SuperHyperVertices are the simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable.

$\begin{matrix} {V_{3}, V_{1}} \\ {V_{3}, V_{2}} \\ {V_{3}, V_{4}} \end{matrix}$

The neutrosophic SuperHyperSets of neutrosophic SuperHyperVertices, ${V_{3}, V_{1}}, {V_{3}, V_{2}}, {V_{3}, V_{4}},$ are the simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. The neutrosophic SuperHyperSets of the neutrosophic SuperHyperVertices, ${V_{3}, V_{1}}, {V_{3}, V_{2}}, {V_{3}, V_{4}},$ are corresponded to a neutrosophic SuperHyperStable $I (N S H G)$ for a neutrosophic SuperHyperGraph $N S H G : (V, E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There’re only two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperStable is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet includes only one neutrosophic SuperHyperVertex. But the neutrosophic SuperHyperSets of neutrosophic SuperHyperVertices, ${V_{3}, V_{1}}, {V_{3}, V_{2}}, {V_{3}, V_{4}},$ don’t have less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable are up. To sum them up, the neutrosophic SuperHyperSets of neutrosophic SuperHyperVertices, ${V_{3}, V_{1}}, {V_{3}, V_{2}}, {V_{3}, V_{4}},$ are the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. Since the neutrosophic SuperHyperSets of the neutrosophic SuperHyperVertices, ${V_{3}, V_{1}}, {V_{3}, V_{2}}, {V_{3}, V_{4}},$ are corresponded to a neutrosophic SuperHyperStable $I (N S H G)$ for a neutrosophic SuperHyperGraph $N S H G : (V, E)$ is the neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common and they are corresponded to a neutrosophic SuperHyperStable. Since They’vethe maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There aren’t only less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSets, ${V_{3}, V_{1}}, {V_{3}, V_{2}}, {V_{3}, V_{4}} .$ Thus the non-obvious neutrosophic SuperHyperStable, ${V_{3}, V_{1}}, {V_{3}, V_{2}}, {V_{3}, V_{4}},$ are up. The obvious simple type-neutrosophic SuperHyperSets of the neutrosophic SuperHyperStable, ${V_{3}, V_{1}}, {V_{3}, V_{2}}, {V_{3}, V_{4}},$ are neutrosophic SuperHyperSets, ${V_{3}, V_{1}}, {V_{3}, V_{2}}, {V_{3}, V_{4}},$ don’t include only less than two neutrosophic SuperHyperVertices in a connected neutrosophic SuperHyperGraph $N S H G : (V, E) .$ It’s interesting to mention that the only obvious simple type-neutrosophic SuperHyperSets of the neutrosophic neutrosophic SuperHyperStable amid those obvious simple type-neutrosophic SuperHyperSets of the neutrosophic SuperHyperStable, is only ${V_{3}, V_{4}} .$
On the Figure 2, the neutrosophic SuperHyperNotion, namely, neutrosophic SuperHyperStable, is up. $E_{1}$ and $E_{3}$ neutrosophic SuperHyperStable are some empty neutrosophic SuperHyperEdges but $E_{2}$ is a loop neutrosophic SuperHyperEdge and $E_{4}$ is an neutrosophic SuperHyperEdge. Thus in the terms of SuperHyperNeighbor, there’s only one neutrosophic SuperHyperEdge, namely, $E_{4} .$ The neutrosophic SuperHyperVertex, $V_{3}$ is isolated means that there’s no neutrosophic SuperHyperEdge has it as an endpoint. Thus neutrosophic SuperHyperVertex, $V_{3},$ is contained in every given neutrosophic SuperHyperStable. All the following neutrosophic SuperHyperSets of neutrosophic SuperHyperVertices are the simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable.

$\begin{matrix} {V_{3}, V_{1}} \\ {V_{3}, V_{2}} \\ {V_{3}, V_{4}} \end{matrix}$

The neutrosophic SuperHyperSets of neutrosophic SuperHyperVertices, ${V_{3}, V_{1}}, {V_{3}, V_{2}}, {V_{3}, V_{4}},$ are the simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. The neutrosophic SuperHyperSets of the neutrosophic SuperHyperVertices, ${V_{3}, V_{1}}, {V_{3}, V_{2}}, {V_{3}, V_{4}},$ are corresponded to a neutrosophic SuperHyperStable $I (N S H G)$ for a neutrosophic SuperHyperGraph $N S H G : (V, E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There’re only two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperStable is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet includes only one neutrosophic SuperHyperVertex. But the neutrosophic SuperHyperSets of neutrosophic SuperHyperVertices, ${V_{3}, V_{1}}, {V_{3}, V_{2}}, {V_{3}, V_{4}},$ don’t have less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable are up. To sum them up, the neutrosophic SuperHyperSets of neutrosophic SuperHyperVertices, ${V_{3}, V_{1}}, {V_{3}, V_{2}}, {V_{3}, V_{4}},$ are the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. Since the neutrosophic SuperHyperSets of the neutrosophic SuperHyperVertices, ${V_{3}, V_{1}}, {V_{3}, V_{2}}, {V_{3}, V_{4}},$ are corresponded to a neutrosophic SuperHyperStable $I (N S H G)$ for a neutrosophic SuperHyperGraph $N S H G : (V, E)$ is the neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common and they are corresponded to a neutrosophic SuperHyperStable. Since They’vethe maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There aren’t only less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSets, ${V_{3}, V_{1}}, {V_{3}, V_{2}}, {V_{3}, V_{4}} .$ Thus the non-obvious neutrosophic SuperHyperStable, ${V_{3}, V_{1}}, {V_{3}, V_{2}}, {V_{3}, V_{4}},$ are up. The obvious simple type-neutrosophic SuperHyperSets of the neutrosophic SuperHyperStable, ${V_{3}, V_{1}}, {V_{3}, V_{2}}, {V_{3}, V_{4}},$ are neutrosophic SuperHyperSets, ${V_{3}, V_{1}}, {V_{3}, V_{2}}, {V_{3}, V_{4}},$ don’t include only less than two neutrosophic SuperHyperVertices in a connected neutrosophic SuperHyperGraph $N S H G : (V, E) .$ It’s interesting to mention that the only obvious simple type-neutrosophic SuperHyperSets of the neutrosophic neutrosophic SuperHyperStable amid those obvious simple type-neutrosophic SuperHyperSets of the neutrosophic SuperHyperStable, is only ${V_{3}, V_{4}} .$
On the Figure 3, the neutrosophic SuperHyperNotion, namely, neutrosophic SuperHyperStable, is up. $E_{1}, E_{2}$ and $E_{3}$ are some empty neutrosophic SuperHyperEdges but $E_{4}$ is an neutrosophic SuperHyperEdge. Thus in the terms of SuperHyperNeighbor, there’s only one neutrosophic SuperHyperEdge, namely, $E_{4} .$ The neutrosophic SuperHyperSets of neutrosophic SuperHyperVertices, ${V_{1}}, {V_{2}}, {V_{3}},$ are the simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. The neutrosophic SuperHyperSets of the neutrosophic SuperHyperVertices, ${V_{1}}, {V_{2}}, {V_{3}},$ are the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There’re only one neutrosophic SuperHyperVertex inside the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperStable aren’t up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet includes only one neutrosophic SuperHyperVertex in a connected neutrosophic SuperHyperGraph $N S H G : (V, E) .$ But the neutrosophic SuperHyperSets of neutrosophic SuperHyperVertices, ${V_{1}}, {V_{2}}, {V_{3}},$ don’t have more than one neutrosophic SuperHyperVertex inside the intended neutrosophic SuperHyperSet. Thus the non-obvious simple type-neutrosophic SuperHyperSets of the neutrosophic SuperHyperStable aren’t up. To sum them up, the neutrosophic SuperHyperSets of neutrosophic SuperHyperVertices, ${V_{1}}, {V_{2}}, {V_{3}},$ aren’t the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. Since the neutrosophic SuperHyperSets of the neutrosophic SuperHyperVertices, ${V_{1}}, {V_{2}}, {V_{3}},$ are corresponded to a neutrosophic SuperHyperStable $I (N S H G)$ for a neutrosophic SuperHyperGraph $N S H G : (V, E)$ is the neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common and they are neutrosophic SuperHyperStable. Since they’vethe maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There are only less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSets, ${V_{1}}, {V_{2}}, {V_{3}} .$ Thus the non-obvious neutrosophic SuperHyperStable, ${V_{1}}, {V_{2}}, {V_{3}},$ aren’t up. The obvious simple type-neutrosophic SuperHyperSets of the neutrosophic SuperHyperStable, ${V_{1}}, {V_{2}}, {V_{3}},$ are the neutrosophic SuperHyperSets, ${V_{1}}, {V_{2}}, {V_{3}},$ don’t include only more than one neutrosophic SuperHyperVertex in a connected neutrosophic SuperHyperGraph $N S H G : (V, E) .$ It’s interesting to mention that the only obvious simple type-neutrosophic SuperHyperSets of the neutrosophic neutrosophic SuperHyperStable amid those obvious simple type-neutrosophic SuperHyperSets of the neutrosophic SuperHyperStable, is only ${V_{3}} .$
On the Figure 4, the neutrosophic SuperHyperNotion, namely, an neutrosophic SuperHyperStable, is up. There’s no empty neutrosophic SuperHyperEdge but $E_{3}$ are a loop neutrosophic SuperHyperEdge on ${F},$ and there are some neutrosophic SuperHyperEdges, namely, $E_{1}$ on ${H, V_{1}, V_{3}},$ alongside $E_{2}$ on ${O, H, V_{4}, V_{3}}$ and $E_{4}, E_{5}$ on ${N, V_{1}, V_{2}, V_{3}, F} .$ The neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{2}, V_{4}},$ is the simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices, ${V_{2}, V_{4}},$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There’re only two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperStable isn’t up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet includes only one neutrosophic SuperHyperVertex since it doesn’t form any kind of pairs titled to SuperHyperNeighbors in a connected neutrosophic SuperHyperGraph $N S H G : (V, E) .$ But the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{2}, V_{4}},$ doesn’t have less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable isn’t up. To sum them up, the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{2}, V_{4}},$ is the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices, ${V_{2}, V_{4}},$ is the neutrosophic SuperHyperSet Ss of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common and it’s neutrosophic SuperHyperStable. Since it’sthe maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There aren’t only less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet, ${V_{2}, V_{4}} .$ Thus the non-obvious neutrosophic SuperHyperStable, ${V_{2}, V_{4}},$ is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable, ${V_{2}, V_{4}},$ is a neutrosophic SuperHyperSet, ${V_{2}, V_{4}},$ doesn’t include only less than two neutrosophic SuperHyperVertices in a connected neutrosophic SuperHyperGraph $N S H G : (V, E) .$
On the Figure 5, the neutrosophic SuperHyperNotion, namely, neutrosophic SuperHyperStable, is up. There’s neither empty neutrosophic SuperHyperEdge nor loop neutrosophic SuperHyperEdge. The neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{2}, V_{6}, V_{9}, V_{15}},$ is the simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices, ${V_{2}, V_{6}, V_{9}, V_{15}},$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There’re only one neutrosophic SuperHyperVertex inside the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperStable is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet includes only one neutrosophic SuperHyperVertex thus it doesn’t form any kind of pairs titled to SuperHyperNeighbors in a connected neutrosophic SuperHyperGraph $N S H G : (V, E) .$ But the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{2}, V_{6}, V_{9}, V_{15}},$ doesn’t have less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is up. To sum them up, the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{2}, V_{6}, V_{9}, V_{15}},$ is the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices, ${V_{2}, V_{6}, V_{9}, V_{15}},$ is the neutrosophic SuperHyperSet Ss of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. and it’s neutrosophic SuperHyperStable. Since it’sthe maximum neutrosophic cardinality of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There aren’t only less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet, ${V_{2}, V_{6}, V_{9}, V_{15}} .$ Thus the non-obvious neutrosophic SuperHyperStable, ${V_{2}, V_{6}, V_{9}, V_{15}},$ is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable, ${V_{2}, V_{6}, V_{9}, V_{15}},$ is a neutrosophic SuperHyperSet, ${V_{2}, V_{6}, V_{9}, V_{15}},$ doesn’t include only less than two neutrosophic SuperHyperVertices in a connected neutrosophic SuperHyperGraph $N S H G : (V, E)$ is mentioned as the SuperHyperModel $N S H G : (V, E)$ in the Figure 5.
On the Figure 6, the neutrosophic SuperHyperNotion, namely, neutrosophic SuperHyperStable, is up. There’s neither empty neutrosophic SuperHyperEdge nor loop neutrosophic SuperHyperEdge. The neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices,

$\begin{matrix} {V_{2}, V_{4}, V_{6}, V_{8}, V_{10}, \\ V_{22}, V_{19}, V_{17}, V_{15}, V_{13},}, \end{matrix}$

is the simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices,

$\begin{matrix} {V_{2}, V_{4}, V_{6}, V_{8}, V_{10}, \\ V_{22}, V_{19}, V_{17}, V_{15}, V_{13},}, \end{matrix}$

is the maximum neutrosophic cardinality of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There’re only only neutrosophic SuperHyperVertex inside the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperStable is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet includes only one neutrosophic SuperHyperVertex doesn’t form any kind of pairs titled to SuperHyperNeighbors in a connected neutrosophic SuperHyperGraph $N S H G : (V, E) .$ But the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices,

$\begin{matrix} {V_{2}, V_{4}, V_{6}, V_{8}, V_{10}, \\ V_{22}, V_{19}, V_{17}, V_{15}, V_{13},}, \end{matrix}$

doesn’t have less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is up. To sum them up, the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices,

$\begin{matrix} {V_{2}, V_{4}, V_{6}, V_{8}, V_{10}, \\ V_{22}, V_{19}, V_{17}, V_{15}, V_{13},}, \end{matrix}$

is the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices,

$\begin{matrix} {V_{2}, V_{4}, V_{6}, V_{8}, V_{10}, \\ V_{22}, V_{19}, V_{17}, V_{15}, V_{13},}, \end{matrix}$

is the neutrosophic SuperHyperSet Ss of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common and it’s a neutrosophic SuperHyperStable. Since it’s the maximum neutrosophic cardinality of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There aren’t only less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet,

$\begin{matrix} {V_{2}, V_{4}, V_{6}, V_{8}, V_{10}, \\ V_{22}, V_{19}, V_{17}, V_{15}, V_{13},}, \end{matrix}$

Thus the non-obvious neutrosophic SuperHyperStable,

$\begin{matrix} {V_{2}, V_{4}, V_{6}, V_{8}, V_{10}, \\ V_{22}, V_{19}, V_{17}, V_{15}, V_{13},}, \end{matrix}$

is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable,

$\begin{matrix} {V_{2}, V_{4}, V_{6}, V_{8}, V_{10}, \\ V_{22}, V_{19}, V_{17}, V_{15}, V_{13},}, \end{matrix}$

is a neutrosophic SuperHyperSet,

$\begin{matrix} {V_{2}, V_{4}, V_{6}, V_{8}, V_{10}, \\ V_{22}, V_{19}, V_{17}, V_{15}, V_{13},}, \end{matrix}$

doesn’t include only less than two neutrosophic SuperHyperVertices in a connected neutrosophic SuperHyperGraph $N S H G : (V, E)$ with a illustrated SuperHyperModeling of the Figure 6.
On the Figure 7, the neutrosophic SuperHyperNotion, namely, neutrosophic SuperHyperStable, is up. There’s neither empty neutrosophic SuperHyperEdge nor loop neutrosophic SuperHyperEdge. The neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{2}, V_{5}, V_{9}},$ is the simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices, ${V_{2}, V_{5}, V_{9}},$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There’re only one neutrosophic SuperHyperVertex inside the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperStable is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet includes only one neutrosophic SuperHyperVertex doesn’t form any kind of pairs are titled to SuperHyperNeighbors in a connected neutrosophic SuperHyperGraph $N S H G : (V, E) .$ But the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{2}, V_{5}, V_{9}},$ doesn’t have less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is up. To sum them up, the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{2}, V_{5}, V_{9}},$ is the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices, ${V_{2}, V_{5}, V_{9}},$ is the neutrosophic SuperHyperSet Ss of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common and it’s a neutrosophic SuperHyperStable. Since it’sthe maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There aren’t only less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet, ${V_{2}, V_{5}, V_{9}} .$ Thus the non-obvious neutrosophic SuperHyperStable, ${V_{2}, V_{5}, V_{9}},$ is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable, ${V_{2}, V_{5}, V_{9}},$ is a neutrosophic SuperHyperSet, ${V_{2}, V_{5}, V_{9}},$ doesn’t include only less than two neutrosophic SuperHyperVertices in a connected neutrosophic SuperHyperGraph $N S H G : (V, E)$ of depicted SuperHyperModel as the Figure 7.
On the Figure 8, the neutrosophic SuperHyperNotion, namely, neutrosophic SuperHyperStable, is up. There’s neither empty neutrosophic SuperHyperEdge nor loop neutrosophic SuperHyperEdge. The neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{2}, V_{5}, V_{8}},$ is the simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices, ${V_{2}, V_{5}, V_{8}},$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There’re not only two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperStable is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet includes only two neutrosophic SuperHyperVertices doesn’t form any kind of pairs are titled to SuperHyperNeighbors in a connected neutrosophic SuperHyperGraph $N S H G : (V, E) .$ But the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{2}, V_{5}, V_{8}},$ doesn’t have less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is up. To sum them up, the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{2}, V_{5}, V_{8}},$ is the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices, ${V_{2}, V_{5}, V_{8}},$ is the neutrosophic SuperHyperSet Ss of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common and it’s a neutrosophic SuperHyperStable. Since it’sthe maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There aren’t only less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet, ${V_{2}, V_{5}, V_{8}},$ Thus the non-obvious neutrosophic SuperHyperStable, ${V_{2}, V_{5}, V_{8}},$ is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable, ${V_{2}, V_{5}, V_{8}},$ is a neutrosophic SuperHyperSet, ${V_{2}, V_{5}, V_{8}},$ doesn’t exclude only more than two neutrosophic SuperHyperVertices in a connected neutrosophic SuperHyperGraph $N S H G : (V, E)$ of dense SuperHyperModel as the Figure 8.
On the Figure 9, the neutrosophic SuperHyperNotion, namely, neutrosophic SuperHyperStable, is up. There’s neither empty neutrosophic SuperHyperEdge nor loop neutrosophic SuperHyperEdge. The neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices,

$\begin{matrix} {V_{2}, V_{4}, V_{6}, V_{8}, V_{10}, \\ V_{22}, V_{19}, V_{17}, V_{15}, V_{13},}, \end{matrix}$

is the simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices,

$\begin{matrix} {V_{2}, V_{4}, V_{6}, V_{8}, V_{10}, \\ V_{22}, V_{19}, V_{17}, V_{15}, V_{13},}, \end{matrix}$

is the maximum neutrosophic cardinality of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There’re only only neutrosophic SuperHyperVertex inside the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperStable is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet includes only one neutrosophic SuperHyperVertex doesn’t form any kind of pairs titled to SuperHyperNeighbors in a connected neutrosophic SuperHyperGraph $N S H G : (V, E) .$ But the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices,

$\begin{matrix} {V_{2}, V_{4}, V_{6}, V_{8}, V_{10}, \\ V_{22}, V_{19}, V_{17}, V_{15}, V_{13},}, \end{matrix}$

doesn’t have less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is up. To sum them up, the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices,

$\begin{matrix} {V_{2}, V_{4}, V_{6}, V_{8}, V_{10}, \\ V_{22}, V_{19}, V_{17}, V_{15}, V_{13},}, \end{matrix}$

is the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices,

$\begin{matrix} {V_{2}, V_{4}, V_{6}, V_{8}, V_{10}, \\ V_{22}, V_{19}, V_{17}, V_{15}, V_{13},}, \end{matrix}$

is the neutrosophic SuperHyperSet Ss of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common and it’s a neutrosophic SuperHyperStable. Since it’s the maximum neutrosophic cardinality of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There aren’t only less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet,

$\begin{matrix} {V_{2}, V_{4}, V_{6}, V_{8}, V_{10}, \\ V_{22}, V_{19}, V_{17}, V_{15}, V_{13},}, \end{matrix}$

Thus the non-obvious neutrosophic SuperHyperStable,

$\begin{matrix} {V_{2}, V_{4}, V_{6}, V_{8}, V_{10}, \\ V_{22}, V_{19}, V_{17}, V_{15}, V_{13},}, \end{matrix}$

is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable,

$\begin{matrix} {V_{2}, V_{4}, V_{6}, V_{8}, V_{10}, \\ V_{22}, V_{19}, V_{17}, V_{15}, V_{13},}, \end{matrix}$

is a neutrosophic SuperHyperSet,

$\begin{matrix} {V_{2}, V_{4}, V_{6}, V_{8}, V_{10}, \\ V_{22}, V_{19}, V_{17}, V_{15}, V_{13},}, \end{matrix}$

doesn’t include only less than two neutrosophic SuperHyperVertices in a connected neutrosophic neutrosophic SuperHyperGraph $N S H G : (V, E)$ with a messy SuperHyperModeling of the Figure 9.
On the Figure 10, the neutrosophic SuperHyperNotion, namely, neutrosophic SuperHyperStable, is up. There’s neither empty neutrosophic SuperHyperEdge nor loop neutrosophic SuperHyperEdge. The neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{2}, V_{5}, V_{8}},$ is the simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices, ${V_{2}, V_{5}, V_{8}},$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There’re not only two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperStable is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet includes only two neutrosophic SuperHyperVertices doesn’t form any kind of pairs are titled to SuperHyperNeighbors in a connected neutrosophic SuperHyperGraph $N S H G : (V, E) .$ But the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{2}, V_{5}, V_{8}},$ doesn’t have less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is up. To sum them up, the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{2}, V_{5}, V_{8}},$ is the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices, ${V_{2}, V_{5}, V_{8}},$ is the neutrosophic SuperHyperSet Ss of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common and it’s a neutrosophic SuperHyperStable. Since it’sthe maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There aren’t only less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet, ${V_{2}, V_{5}, V_{8}},$ Thus the non-obvious neutrosophic SuperHyperStable, ${V_{2}, V_{5}, V_{8}},$ is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable, ${V_{2}, V_{5}, V_{8}},$ is a neutrosophic SuperHyperSet, ${V_{2}, V_{5}, V_{8}},$ doesn’t exclude only more than two neutrosophic SuperHyperVertices in a connected neutrosophic SuperHyperGraph $N S H G : (V, E)$ of highly-embedding-connected SuperHyperModel as the Figure 10.
On the Figure 11, the neutrosophic SuperHyperNotion, namely, neutrosophic SuperHyperStable, is up. There’s neither empty neutrosophic SuperHyperEdge nor loop neutrosophic SuperHyperEdge. The neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{2}, V_{5}},$ is the simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices, ${V_{2}, V_{5}},$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There’re only two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperStable is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet includes only less than two neutrosophic SuperHyperVertices don’t form any kind of pairs are titled to SuperHyperNeighbors in a connected neutrosophic SuperHyperGraph $N S H G : (V, E) .$ But the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{2}, V_{5}},$ doesn’t have less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is up. To sum them up, the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{2}, V_{5}},$ is the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices, ${V_{2}, V_{5}},$ is the neutrosophic SuperHyperSet Ss of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common and it’s a neutrosophic SuperHyperStable. Since it’sthe maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There aren’t only less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet, ${V_{2}, V_{5}} .$ Thus the non-obvious neutrosophic SuperHyperStable, ${V_{2}, V_{5}},$ is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable, ${V_{2}, V_{5}},$ is a neutrosophic SuperHyperSet, ${V_{2}, V_{5}},$ doesn’t include only less than two neutrosophic SuperHyperVertices in a connected neutrosophic SuperHyperGraph $N S H G : (V, E) .$
On the Figure 12, the neutrosophic SuperHyperNotion, namely, neutrosophic SuperHyperStable, is up. There’s neither empty neutrosophic SuperHyperEdge nor loop neutrosophic SuperHyperEdge. The neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{1}, V_{2}, V_{3}, V_{7}, V_{8}},$ is the simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices, ${V_{1}, V_{2}, V_{3}, V_{7}, V_{8}},$ is the maximum neutrosophic cardinality of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There’re not only two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperStable is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet includes only two neutrosophic SuperHyperVertices doesn’t form any kind of pairs are titled to SuperHyperNeighbors in a connected neutrosophic SuperHyperGraph $N S H G : (V, E) .$ But the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{1}, V_{2}, V_{3}, V_{7}, V_{8}},$ doesn’t have less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is up. To sum them up, the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{1}, V_{2}, V_{3}, V_{7}, V_{8}},$ is the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices, ${V_{1}, V_{2}, V_{3}, V_{7}, V_{8}},$ is the neutrosophic SuperHyperSet Ss of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common and they are neutrosophic SuperHyperStable. Since it’sthe maximum neutrosophic cardinality of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There aren’t only less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet, ${V_{1}, V_{2}, V_{3}, V_{7}, V_{8}} .$ Thus the non-obvious neutrosophic SuperHyperStable, ${V_{1}, V_{2}, V_{3}, V_{7}, V_{8}},$ is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable, ${V_{1}, V_{2}, V_{3}, V_{7}, V_{8}},$ is a neutrosophic SuperHyperSet, ${V_{1}, V_{2}, V_{3}, V_{7}, V_{8}},$ doesn’t include only more than one neutrosophic SuperHyperVertex in a connected neutrosophic SuperHyperGraph $N S H G : (V, E)$ in highly-multiple-connected-style SuperHyperModel On the Figure 12.
On the Figure 13, the neutrosophic SuperHyperNotion, namely, neutrosophic SuperHyperStable, is up. There’s neither empty neutrosophic SuperHyperEdge nor loop neutrosophic SuperHyperEdge. The neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{2}, V_{5}},$ is the simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices, ${V_{2}, V_{5}},$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There’re only two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperStable is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet includes only less than two neutrosophic SuperHyperVertices don’t form any kind of pairs are titled to SuperHyperNeighbors in a connected neutrosophic SuperHyperGraph $N S H G : (V, E) .$ But the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{2}, V_{5}},$ doesn’t have less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is up. To sum them up, the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{2}, V_{5}},$ is the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices, ${V_{2}, V_{5}},$ is the neutrosophic SuperHyperSet Ss of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common and it’s a neutrosophic SuperHyperStable. Since it’sthe maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There aren’t only less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet, ${V_{2}, V_{5}} .$ Thus the non-obvious neutrosophic SuperHyperStable, ${V_{2}, V_{5}},$ is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable, ${V_{2}, V_{5}},$ is a neutrosophic SuperHyperSet, ${V_{2}, V_{5}},$ doesn’t include only less than two neutrosophic SuperHyperVertices in a connected neutrosophic SuperHyperGraph $N S H G : (V, E) .$
On the Figure 14, the neutrosophic SuperHyperNotion, namely, neutrosophic SuperHyperStable, is up. There’s neither empty neutrosophic SuperHyperEdge nor loop neutrosophic SuperHyperEdge. The neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{3}, V_{2}},$ is the simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices, ${V_{3}, V_{2}},$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There’re only two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperStable is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet includes only less than two neutrosophic SuperHyperVertices don’t form any kind of pairs are titled to SuperHyperNeighbors in a connected neutrosophic SuperHyperGraph $N S H G : (V, E) .$ But the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{3}, V_{2}},$ doesn’t have less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is up. To sum them up, the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{3}, V_{2}},$ is the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices, ${V_{3}, V_{2}},$ is the neutrosophic SuperHyperSet Ss of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common and it’s a neutrosophic SuperHyperStable. Since it’sthe maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There aren’t only less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet, ${V_{3}, V_{2}} .$ Thus the non-obvious neutrosophic SuperHyperStable, ${V_{3}, V_{2}},$ is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable, ${V_{3}, V_{2}},$ is a neutrosophic SuperHyperSet, ${V_{3}, V_{2}},$ doesn’t include only less than two neutrosophic SuperHyperVertices in a connected neutrosophic SuperHyperGraph $N S H G : (V, E) .$
On the Figure 15, the neutrosophic SuperHyperNotion, namely, neutrosophic SuperHyperStable, is up. There’s neither empty neutrosophic SuperHyperEdge nor loop neutrosophic SuperHyperEdge. The neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{5}, V_{2}, V_{6}},$ is the simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices, ${V_{5}, V_{2}, V_{6}},$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There’re only two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperStable is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet includes only less than two neutrosophic SuperHyperVertices don’t form any kind of pairs are titled to SuperHyperNeighbors in a connected neutrosophic SuperHyperGraph $N S H G : (V, E) .$ But the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{5}, V_{2}, V_{6}},$ doesn’t have less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is up. To sum them up, the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{5}, V_{2}, V_{6}},$ is the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices, ${V_{5}, V_{2}, V_{6}},$ is the neutrosophic SuperHyperSet Ss of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common and it’s a neutrosophic SuperHyperStable. Since it’sthe maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There aren’t only less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet, ${V_{5}, V_{2}, V_{6}} .$ Thus the non-obvious neutrosophic SuperHyperStable, ${V_{5}, V_{2}, V_{6}},$ is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable, ${V_{5}, V_{2}, V_{6}},$ is a neutrosophic SuperHyperSet, ${V_{5}, V_{2}, V_{6}},$ doesn’t include only less than two neutrosophic SuperHyperVertices in a connected neutrosophic SuperHyperGraph $N S H G : (V, E)$ as Linearly-Connected SuperHyperModel On the Figure 15.
On the Figure 16, the neutrosophic SuperHyperNotion, namely, neutrosophic SuperHyperStable, is up. There’s neither empty neutrosophic SuperHyperEdge nor loop neutrosophic SuperHyperEdge. The neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{1}, V_{2}, V_{8}, V_{22}},$ is the simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices, ${V_{1}, V_{2}, V_{8}, V_{22}},$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There’re only two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperStable is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet includes only less than two neutrosophic SuperHyperVertices don’t form any kind of pairs are titled to SuperHyperNeighbors in a connected neutrosophic SuperHyperGraph $N S H G : (V, E) .$ But the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{1}, V_{2}, V_{8}, V_{22}},$ doesn’t have less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is up. To sum them up, the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{1}, V_{2}, V_{8}, V_{22}},$ is the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices, ${V_{1}, V_{2}, V_{8}, V_{22}},$ is the neutrosophic SuperHyperSet Ss of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common and it’s a neutrosophic SuperHyperStable. Since it’sthe maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There aren’t only less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet, ${V_{1}, V_{2}, V_{8}, V_{22}} .$ Thus the non-obvious neutrosophic SuperHyperStable, ${V_{1}, V_{2}, V_{8}, V_{22}},$ is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable, ${V_{1}, V_{2}, V_{8}, V_{22}},$ is a neutrosophic SuperHyperSet, ${V_{1}, V_{2}, V_{8}, V_{22}},$ doesn’t include only less than two neutrosophic SuperHyperVertices in a connected neutrosophic SuperHyperGraph $N S H G : (V, E) .$
On the Figure 17, the neutrosophic SuperHyperNotion, namely, neutrosophic SuperHyperStable, is up. There’s neither empty neutrosophic SuperHyperEdge nor loop neutrosophic SuperHyperEdge. The neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{1}, V_{2}, V_{8}, V_{22}},$ is the simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices, ${V_{1}, V_{2}, V_{8}, V_{22}},$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There’re only two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperStable is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet includes only less than two neutrosophic SuperHyperVertices don’t form any kind of pairs are titled to SuperHyperNeighbors in a connected neutrosophic SuperHyperGraph $N S H G : (V, E) .$ But the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{1}, V_{2}, V_{8}, V_{22}},$ doesn’t have less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is up. To sum them up, the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{1}, V_{2}, V_{8}, V_{22}},$ is the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices, ${V_{1}, V_{2}, V_{8}, V_{22}},$ is the neutrosophic SuperHyperSet Ss of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common and it’s a neutrosophic SuperHyperStable. Since it’sthe maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There aren’t only less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet, ${V_{1}, V_{2}, V_{8}, V_{22}} .$ Thus the non-obvious neutrosophic SuperHyperStable, ${V_{1}, V_{2}, V_{8}, V_{22}},$ is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable, ${V_{1}, V_{2}, V_{8}, V_{22}},$ is a neutrosophic SuperHyperSet, ${V_{1}, V_{2}, V_{8}, V_{22}},$ doesn’t include only less than two neutrosophic SuperHyperVertices in a connected neutrosophic SuperHyperGraph $N S H G : (V, E)$ as Lnearly-over-packed SuperHyperModel is featured On the Figure 17.
On the Figure 18, the neutrosophic SuperHyperNotion, namely, neutrosophic SuperHyperStable, is up. There’s neither empty neutrosophic SuperHyperEdge nor loop neutrosophic SuperHyperEdge. The neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{2}},$ is the simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices, ${V_{2}},$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There’s only one neutrosophic SuperHyperVertex inside the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperStable isn’t up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet includes only less than two neutrosophic SuperHyperVertices don’t form any kind of pairs are titled to SuperHyperNeighbors in a connected neutrosophic SuperHyperGraph $N S H G : (V, E) .$ But the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{2}},$ does has less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable isn’t up. To sum them up, the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{2}},$ isn’t the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices, ${V_{2}},$ is the neutrosophic SuperHyperSet Ss of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common and it’s a neutrosophic SuperHyperStable. Since it’sthe maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There’s only less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet, ${V_{2}} .$ Thus the non-obvious neutrosophic SuperHyperStable, ${V_{2}},$ isn’t up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable, ${V_{2}},$ is a neutrosophic SuperHyperSet, ${V_{2}},$ does includes only less than two neutrosophic SuperHyperVertices in a connected neutrosophic SuperHyperGraph $N S H G : (V, E)$
On the Figure 19, the neutrosophic SuperHyperNotion, namely, neutrosophic SuperHyperStable, is up. There’s neither empty neutrosophic SuperHyperEdge nor loop neutrosophic SuperHyperEdge. The neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{1}, O_{6}, V_{9}, V_{5}},$ is the simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices, ${V_{1}, O_{6}, V_{9}, V_{5}},$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There’re only two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperStable is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet includes only less than two neutrosophic SuperHyperVertices don’t form any kind of pairs are titled to SuperHyperNeighbors in a connected neutrosophic SuperHyperGraph $N S H G : (V, E) .$ But the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{1}, O_{6}, V_{9}, V_{5}},$ doesn’t have less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is up. To sum them up, the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{1}, O_{6}, V_{9}, V_{5}},$ is the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices, ${V_{1}, O_{6}, V_{9}, V_{5}},$ is the neutrosophic SuperHyperSet Ss of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common and it’s a neutrosophic SuperHyperStable. Since it’sthe maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There aren’t only less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet, ${V_{1}, O_{6}, V_{9}, V_{5}} .$ Thus the non-obvious neutrosophic SuperHyperStable, ${V_{1}, O_{6}, V_{9}, V_{5}},$ is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable, ${V_{1}, O_{6}, V_{9}, V_{5}},$ is a neutrosophic SuperHyperSet, ${V_{1}, O_{6}, V_{9}, V_{5}},$ doesn’t include only less than two neutrosophic SuperHyperVertices in a connected neutrosophic SuperHyperGraph $N S H G : (V, E) .$
On the Figure 20, the neutrosophic SuperHyperNotion, namely, neutrosophic SuperHyperStable, is up. There’s neither empty neutrosophic SuperHyperEdge nor loop neutrosophic SuperHyperEdge. The neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{1}, V_{3}, V_{5}, R_{9}, V_{6}, V_{9}, S_{9}, V_{10}, P_{4}, T_{4}},$ is the simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices, ${V_{1}, V_{3}, V_{5}, R_{9}, V_{6}, V_{9}, S_{9}, V_{10}, P_{4}, T_{4}},$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There’re only two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperStable is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet includes only less than two neutrosophic SuperHyperVertices don’t form any kind of pairs are titled to SuperHyperNeighbors in a connected neutrosophic SuperHyperGraph $N S H G : (V, E) .$ But the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{1}, V_{3}, V_{5}, R_{9}, V_{6}, V_{9}, S_{9}, V_{10}, P_{4}, T_{4}},$ doesn’t have less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable is up. To sum them up, the neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices, ${V_{1}, V_{3}, V_{5}, R_{9}, V_{6}, V_{9}, S_{9}, V_{10}, P_{4}, T_{4}},$ is the non-obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices, ${V_{1}, V_{3}, V_{5}, R_{9}, V_{6}, V_{9}, S_{9}, V_{10}, P_{4}, T_{4}},$ is the neutrosophic SuperHyperSet Ss of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common and it’s a neutrosophic SuperHyperStable. Since it’sthe maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. There aren’t only less than two neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet, ${V_{1}, V_{3}, V_{5}, R_{9}, V_{6}, V_{9}, S_{9}, V_{10}, P_{4}, T_{4}} .$ Thus the non-obvious neutrosophic SuperHyperStable, ${V_{1}, V_{3}, V_{5}, R_{9}, V_{6}, V_{9}, S_{9}, V_{10}, P_{4}, T_{4}},$ is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable, ${V_{1}, V_{3}, V_{5}, R_{9}, V_{6}, V_{9}, S_{9}, V_{10}, P_{4}, T_{4}},$ is a neutrosophic SuperHyperSet, ${V_{1}, V_{3}, V_{5}, R_{9}, V_{6}, V_{9}, S_{9}, V_{10}, P_{4}, T_{4}},$ doesn’t include only less than two neutrosophic SuperHyperVertices in a connected neutrosophic SuperHyperGraph $N S H G : (V, E) .$

Figure 1. The neutrosophic SuperHyperGraphs Associated to the Notions of neutrosophic SuperHyperStable in the Example 2.1.

Figure 2. The neutrosophic SuperHyperGraphs Associated to the Notions of neutrosophic SuperHyperStable in the Example 2.1.

Figure 3. The neutrosophic SuperHyperGraphs Associated to the Notions of neutrosophic SuperHyperStable in the Example 2.1.

Figure 4. The neutrosophic SuperHyperGraphs Associated to the Notions of neutrosophic SuperHyperStable in the Example 2.1.

Figure 5. The neutrosophic SuperHyperGraphs Associated to the Notions of neutrosophic SuperHyperStable in the Example 2.1.

Figure 6. The neutrosophic SuperHyperGraphs Associated to the Notions of neutrosophic SuperHyperStable in the Example 2.1.

Figure 7. The neutrosophic SuperHyperGraphs Associated to the Notions of neutrosophic SuperHyperStable in the Example 2.1.

Figure 8. The neutrosophic SuperHyperGraphs Associated to the Notions of neutrosophic SuperHyperStable in the Example 2.1.

Figure 9. The neutrosophic SuperHyperGraphs Associated to the Notions of neutrosophic SuperHyperStable in the Example 2.1.

Figure 10. The neutrosophic SuperHyperGraphs Associated to the Notions of neutrosophic SuperHyperStable in the Example 2.1.

Figure 11. The neutrosophic SuperHyperGraphs Associated to the Notions of neutrosophic SuperHyperStable in the Example 2.1.

Figure 12. The neutrosophic SuperHyperGraphs Associated to the Notions of neutrosophic SuperHyperStable in the Example 2.1.

Figure 13. The neutrosophic SuperHyperGraphs Associated to the Notions of neutrosophic SuperHyperStable in the Example 2.1.

Figure 14. The neutrosophic SuperHyperGraphs Associated to the Notions of neutrosophic SuperHyperStable in the Example 2.1.

Figure 15. The neutrosophic SuperHyperGraphs Associated to the Notions of neutrosophic SuperHyperStable in the Example 2.1.

Figure 16. The neutrosophic SuperHyperGraphs Associated to the Notions of neutrosophic SuperHyperStable in the Example 2.1.

Figure 17. The neutrosophic SuperHyperGraphs Associated to the Notions of neutrosophic SuperHyperStable in the Example 2.1.

Figure 18. The neutrosophic SuperHyperGraphs Associated to the Notions of neutrosophic SuperHyperStable in the Example 2.1.

Figure 19. The neutrosophic SuperHyperGraphs Associated to the Notions of neutrosophic SuperHyperStable in the Example 2.1.

Figure 20. The neutrosophic SuperHyperGraphs Associated to the Notions of neutrosophic SuperHyperStable in the Example 2.1.

Proposition 2.2.

Assume a connected neutrosophic SuperHyperGraph

N S H G : (V, E) .

Then in the worst case, literally,

V ∖ V ∖ {z},

is a neutrosophic SuperHyperStable. In other words, the least neutrosophic cardinality, the lower sharp bound for the neutrosophic cardinality, of a neutrosophic SuperHyperStable is the neutrosophic cardinality of

V ∖ V ∖ {z} .

Proof.

Assume a connected neutrosophic SuperHyperGraph

N S H G : (V, E) .

The neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices

V ∖ V ∖ {}

is a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common but it isn’t an neutrosophic SuperHyperStable. Since it doesn’t have the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices

V ∖ V ∖ {x, z}

is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices but it isn’t a neutrosophic SuperHyperStable. Since it doesn’t do the procedure such that such that there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. [there’s at least one neutrosophic SuperHyperVertex inside implying there’s, sometimes in the connected neutrosophic SuperHyperGraph

N S H G : (V, E),

a neutrosophic SuperHyperVertex, titled its SuperHyperNeighbor, to that neutrosophic SuperHyperVertex in the neutrosophic SuperHyperSet S so as S doesn’t do “the procedure”.]. There’s only one neutrosophic SuperHyperVertex inside the intended neutrosophic SuperHyperSet,

V ∖ V ∖ {z} .

Thus the obvious neutrosophic SuperHyperStable,

V ∖ V ∖ {z},

is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable,

V ∖ V ∖ {z},

is a neutrosophic SuperHyperSet,

V ∖ V ∖ {z},

includes only one neutrosophic SuperHyperVertex doesn’t form any kind of pairs are titled SuperHyperNeighbors in a connected neutrosophic SuperHyperGraph

N S H G : (V, E) .

Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices

V ∖ V ∖ {z},

is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that

V (G)

there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. □

Proposition 2.3.

Assume a connected neutrosophic SuperHyperGraph

N S H G : (V, E) .

Then the extreme number of neutrosophic SuperHyperStable has, the least neutrosophic cardinality, the lower sharp bound for neutrosophic cardinality, is the extreme neutrosophic cardinality of

V ∖ V ∖ {z}

if there’s an neutrosophic SuperHyperStable with the least neutrosophic cardinality, the lower sharp bound for neutrosophic cardinality.

Proof.

Assume a connected neutrosophic SuperHyperGraph

N S H G : (V, E) .

Consider there’s an neutrosophic SuperHyperStable with the least neutrosophic cardinality, the lower sharp bound for neutrosophic cardinality. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices

V ∖ V ∖ {}

V ∖ V ∖ {x, z}

N S H G : (V, E),

V ∖ V ∖ {z} .

Thus the obvious neutrosophic SuperHyperStable,

V ∖ V ∖ {z},

is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable,

V ∖ V ∖ {z},

is a neutrosophic SuperHyperSet,

V ∖ V ∖ {z},

includes only one neutrosophic SuperHyperVertex doesn’t form any kind of pairs are titled SuperHyperNeighbors in a connected neutrosophic SuperHyperGraph

N S H G : (V, E) .

Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices

V ∖ V ∖ {z},

is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that

V (G)

there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. Then the extreme number of neutrosophic SuperHyperStable has, the least neutrosophic cardinality, the lower sharp bound for neutrosophic cardinality, is the extreme neutrosophic cardinality of

V ∖ V ∖ {z}

if there’s an neutrosophic SuperHyperStable with the least neutrosophic cardinality, the lower sharp bound for neutrosophic cardinality. □

Proposition 2.4.

Assume a connected neutrosophic SuperHyperGraph

N S H G : (V, E) .

If a neutrosophic SuperHyperEdge has z neutrosophic SuperHyperVertices, then

z - 1

number of those interior neutrosophic SuperHyperVertices from that neutrosophic SuperHyperEdge exclude to any neutrosophic SuperHyperStable.

Proof.

Assume a connected neutrosophic SuperHyperGraph

N S H G : (V, E) .

Let a neutrosophic SuperHyperEdge has z neutrosophic SuperHyperVertices. Consider

z - 2

number of those neutrosophic SuperHyperVertices from that neutrosophic SuperHyperEdge exclude to any given neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices. Consider there’s an neutrosophic SuperHyperStable with the least neutrosophic cardinality, the lower sharp bound for neutrosophic cardinality. Assume a connected neutrosophic SuperHyperGraph

N S H G : (V, E) .

The neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices

V ∖ V ∖ {}

V ∖ V ∖ {x, z}

N S H G : (V, E),

V ∖ V ∖ {z} .

Thus the obvious neutrosophic SuperHyperStable,

V ∖ V ∖ {z},

is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable,

V ∖ V ∖ {z},

is a neutrosophic SuperHyperSet,

V ∖ V ∖ {z},

includes only one neutrosophic SuperHyperVertex doesn’t form any kind of pairs are titled SuperHyperNeighbors in a connected neutrosophic SuperHyperGraph

N S H G : (V, E) .

Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices

V ∖ V ∖ {z},

is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that

V (G)

there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. Thus, if a neutrosophic SuperHyperEdge has z neutrosophic SuperHyperVertices, then

z - 1

number of those interior neutrosophic SuperHyperVertices from that neutrosophic SuperHyperEdge exclude to any neutrosophic SuperHyperStable. □

Proposition 2.5.

Assume a connected neutrosophic SuperHyperGraph

N S H G : (V, E) .

There’s not any neutrosophic SuperHyperEdge has only more than one distinct interior neutrosophic SuperHyperVertex inside of any given neutrosophic SuperHyperStable. In other words, there’s not an unique neutrosophic SuperHyperEdge has only two distinct neutrosophic SuperHyperVertices in a neutrosophic SuperHyperStable.

Proof.

Assume a connected neutrosophic SuperHyperGraph

N S H G : (V, E) .

Let a neutrosophic SuperHyperEdge has some neutrosophic SuperHyperVertices. Consider some numbers of those neutrosophic SuperHyperVertices from that neutrosophic SuperHyperEdge excluding more than one distinct neutrosophic SuperHyperVertex, exclude to any given neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices. Consider there’s an neutrosophic SuperHyperStable with the least neutrosophic cardinality, the lower sharp bound for neutrosophic cardinality. Assume a connected neutrosophic SuperHyperGraph

N S H G : (V, E) .

The neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices

V ∖ V ∖ {}

V ∖ V ∖ {x, z}

N S H G : (V, E),

V ∖ V ∖ {z} .

Thus the obvious neutrosophic SuperHyperStable,

V ∖ V ∖ {z},

is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable,

V ∖ V ∖ {z},

is a neutrosophic SuperHyperSet,

V ∖ V ∖ {z},

includes only one neutrosophic SuperHyperVertex doesn’t form any kind of pairs are titled SuperHyperNeighbors in a connected neutrosophic SuperHyperGraph

N S H G : (V, E) .

Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices

V ∖ V ∖ {z},

is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that

V (G)

there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. Thus, there’s not any neutrosophic SuperHyperEdge has only more than one distinct interior neutrosophic SuperHyperVertex inside of any given neutrosophic SuperHyperStable. In other words, there’s not an unique neutrosophic SuperHyperEdge has only two distinct neutrosophic SuperHyperVertices in a neutrosophic SuperHyperStable. □

Proposition 2.6.

Assume a connected neutrosophic SuperHyperGraph

N S H G : (V, E) .

The all interior neutrosophic SuperHyperVertices belong to any neutrosophic SuperHyperStable if for any of them, there’s no other corresponded neutrosophic SuperHyperVertex such that the two interior neutrosophic SuperHyperVertices are mutually SuperHyperNeighbors.

Proof.

Let a neutrosophic SuperHyperEdge has some neutrosophic SuperHyperVertices. Consider all numbers of those neutrosophic SuperHyperVertices from that neutrosophic SuperHyperEdge excluding one distinct neutrosophic SuperHyperVertex, exclude to any given neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices. Consider there’s an neutrosophic SuperHyperStable with the least neutrosophic cardinality, the lower sharp bound for neutrosophic cardinality. Assume a connected neutrosophic SuperHyperGraph

N S H G : (V, E) .

The neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices

V ∖ V ∖ {}

V ∖ V ∖ {x, z}

N S H G : (V, E),

V ∖ V ∖ {z} .

Thus the obvious neutrosophic SuperHyperStable,

V ∖ V ∖ {z},

is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable,

V ∖ V ∖ {z},

is a neutrosophic SuperHyperSet,

V ∖ V ∖ {z},

includes only one neutrosophic SuperHyperVertex doesn’t form any kind of pairs are titled SuperHyperNeighbors in a connected neutrosophic SuperHyperGraph

N S H G : (V, E) .

Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices

V ∖ V ∖ {z},

is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that

V (G)

there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. Thus, the all interior neutrosophic SuperHyperVertices belong to any neutrosophic SuperHyperStable if for any of them, there’s no other corresponded neutrosophic SuperHyperVertex such that the two interior neutrosophic SuperHyperVertices are mutually SuperHyperNeighbors. □

Proposition 2.7.

Assume a connected neutrosophic SuperHyperGraph

N S H G : (V, E) .

The any neutrosophic SuperHyperStable only contains all interior neutrosophic SuperHyperVertices and all exterior neutrosophic SuperHyperVertices where there’s any of them has no SuperHyperNeighbors in and there’s no SuperHyperNeighborhoods in but everything is possible about SuperHyperNeighborhoods and SuperHyperNeighbors out.

Proof.

Assume a connected neutrosophic SuperHyperGraph

N S H G : (V, E) .

N S H G : (V, E) .

The neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices

V ∖ V ∖ {}

V ∖ V ∖ {x, z}

N S H G : (V, E),

V ∖ V ∖ {z} .

Thus the obvious neutrosophic SuperHyperStable,

V ∖ V ∖ {z},

is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable,

V ∖ V ∖ {z},

is a neutrosophic SuperHyperSet,

V ∖ V ∖ {z},

includes only one neutrosophic SuperHyperVertex doesn’t form any kind of pairs are titled SuperHyperNeighbors in a connected neutrosophic SuperHyperGraph

N S H G : (V, E) .

Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices

V ∖ V ∖ {z},

is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that

V (G)

there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. Thus, the any neutrosophic SuperHyperStable only contains all interior neutrosophic SuperHyperVertices and all exterior neutrosophic SuperHyperVertices where there’s any of them has no SuperHyperNeighbors in and there’s no SuperHyperNeighborhoods in but everything is possible about SuperHyperNeighborhoods and SuperHyperNeighbors out. □

Remark 2.8.

The words “ neutrosophic SuperHyperStable” and “SuperHyperDominating” refer to the maximum type-style and the minimum type-style. In other words, they refer to both the maximum[minimum] number and the neutrosophic SuperHyperSet with the maximum[minimum] neutrosophic cardinality.

Proposition 2.9.

Assume a connected neutrosophic SuperHyperGraph

N S H G : (V, E) .

Consider a SuperHyperDominating. Then a neutrosophic SuperHyperStable is either in or out.

Proof.

Assume a connected neutrosophic SuperHyperGraph

N S H G : (V, E) .

Consider a SuperHyperDominating. By applying the Proposition 2.7, the results are up. Thus on a connected neutrosophic SuperHyperGraph

N S H G : (V, E),

and in a SuperHyperDominating. Then a neutrosophic SuperHyperStable is either in or out. □

3. Results on Neutrosophic SuperHyperClasses

Proposition 3.1.

Assume a connected SuperHyperPath

N S H P : (V, E) .

Then a neutrosophic SuperHyperStable-style with the maximum SuperHyperneutrosophic cardinality is a neutrosophic SuperHyperSet of the interior neutrosophic SuperHyperVertices.

Proposition 3.2.

Assume a connected SuperHyperPath

N S H P : (V, E) .

Then a neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet of the interior neutrosophic SuperHyperVertices with only all exceptions in the form of interior neutrosophic SuperHyperVertices from the common neutrosophic SuperHyperEdges. An neutrosophic SuperHyperStable has the number of all the interior neutrosophic SuperHyperVertices minus their SuperHyperNeighborhoods.

Proof.

Assume a connected SuperHyperPath

N S H P : (V, E) .

N S H G : (V, E) .

The neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices

V ∖ V ∖ {}

V ∖ V ∖ {x, z}

N S H G : (V, E),

V ∖ V ∖ {z} .

Thus the obvious neutrosophic SuperHyperStable,

V ∖ V ∖ {z},

is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable,

V ∖ V ∖ {z},

is a neutrosophic SuperHyperSet,

V ∖ V ∖ {z},

includes only one neutrosophic SuperHyperVertex doesn’t form any kind of pairs are titled SuperHyperNeighbors in a connected neutrosophic SuperHyperGraph

N S H G : (V, E) .

Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices

V ∖ V ∖ {z},

is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that

V (G)

there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. Thus, in a connected SuperHyperPath

N S H P : (V, E),

a neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet of the interior neutrosophic SuperHyperVertices with only all exceptions in the form of interior neutrosophic SuperHyperVertices from the common neutrosophic SuperHyperEdges. An neutrosophic SuperHyperStable has the number of all the interior neutrosophic SuperHyperVertices minus their SuperHyperNeighborhoods. □

Example 3.3.

In the Figure 21, the connected SuperHyperPath

N S H P : (V, E),

is highlighted and featured. The neutrosophic SuperHyperSet,

{V_{27}, V_{2}, V_{7}, V_{12}, V_{22}},

of the neutrosophic SuperHyperVertices of the connected SuperHyperPath

N S H P : (V, E),

in the SuperHyperModel Figure 21, is the neutrosophic SuperHyperStable.

Proposition 3.4.

Assume a connected SuperHyperCycle

N S H C : (V, E) .

Then a neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet of the interior neutrosophic SuperHyperVertices with only all exceptions in the form of interior neutrosophic SuperHyperVertices from the same SuperHyperNeighborhoods. A neutrosophic SuperHyperStable has the number of all the neutrosophic SuperHyperEdges and the lower bound is the half number of all the neutrosophic SuperHyperEdges.

Proof.

Assume a connected SuperHyperCycle

N S H C : (V, E) .

N S H G : (V, E) .

The neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices

V ∖ V ∖ {}

V ∖ V ∖ {x, z}

N S H G : (V, E),

V ∖ V ∖ {z} .

Thus the obvious neutrosophic SuperHyperStable,

V ∖ V ∖ {z},

is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable,

V ∖ V ∖ {z},

is a neutrosophic SuperHyperSet,

V ∖ V ∖ {z},

includes only one neutrosophic SuperHyperVertex doesn’t form any kind of pairs are titled SuperHyperNeighbors in a connected neutrosophic SuperHyperGraph

N S H G : (V, E) .

Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices

V ∖ V ∖ {z},

is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that

V (G)

there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. Thus, in a connected SuperHyperCycle

N S H C : (V, E),

a neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet of the interior neutrosophic SuperHyperVertices with only all exceptions in the form of interior neutrosophic SuperHyperVertices from the same SuperHyperNeighborhoods. A neutrosophic SuperHyperStable has the number of all the neutrosophic SuperHyperEdges and the lower bound is the half number of all the neutrosophic SuperHyperEdges. □

Example 3.5.

In the Figure 22, the connected SuperHyperCycle

N S H C : (V, E),

is highlighted and featured. The obtained neutrosophic SuperHyperSet, by the Algorithm in previous result, of the neutrosophic SuperHyperVertices of the connected SuperHyperCycle

N S H C : (V, E),

in the SuperHyperModel Figure 22,

\begin{matrix} {{P_{13}, J_{13}, K_{13}, H_{13}}, \\ {Z_{13}, W_{13}, V_{13}}, {U_{14}, T_{14}, R_{14}, S_{14}}, \\ {P_{15}, J_{15}, K_{15}, R_{15}}, \\ {J_{5}, O_{5}, K_{5}, L_{5}}, {J_{5}, O_{5}, K_{5}, L_{5}}, V_{3}, \\ {U_{6}, H_{7}, J_{7}, K_{7}, O_{7}, L_{7}, P_{7}}, {T_{8}, U_{8}, V_{8}, S_{8}}, \\ {T_{9}, K_{9}, J_{9}}, {H_{10}, J_{10}, E_{10}, R_{10}, W_{9}}, \\ {S_{11}, R_{11}, O_{11}, L_{11}}, \\ {U_{12}, V_{12}, W_{12}, Z_{12}, O_{12}}}, \end{matrix}

is the neutrosophic SuperHyperStable.

Proposition 3.6.

Assume a connected SuperHyperStar

N S H S : (V, E) .

Then a neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet of the interior neutrosophic SuperHyperVertices, excluding the SuperHyperCenter, with only all exceptions in the form of interior neutrosophic SuperHyperVertices from common neutrosophic SuperHyperEdge. An neutrosophic SuperHyperStable has the number of the neutrosophic cardinality of the second SuperHyperPart.

Proof.

Assume a connected SuperHyperStar

N S H S : (V, E) .

N S H G : (V, E) .

The neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices

V ∖ V ∖ {}

V ∖ V ∖ {x, z}

N S H G : (V, E),

V ∖ V ∖ {z} .

Thus the obvious neutrosophic SuperHyperStable,

V ∖ V ∖ {z},

is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable,

V ∖ V ∖ {z},

is a neutrosophic SuperHyperSet,

V ∖ V ∖ {z},

includes only one neutrosophic SuperHyperVertex doesn’t form any kind of pairs are titled SuperHyperNeighbors in a connected neutrosophic SuperHyperGraph

N S H G : (V, E) .

Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices

V ∖ V ∖ {z},

is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that

V (G)

there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. Thus, in a connected SuperHyperStar

N S H S : (V, E),

a neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet of the interior neutrosophic SuperHyperVertices, excluding the SuperHyperCenter, with only all exceptions in the form of interior neutrosophic SuperHyperVertices from common neutrosophic SuperHyperEdge. An neutrosophic SuperHyperStable has the number of the neutrosophic cardinality of the second SuperHyperPart. □

Example 3.7.

In the Figure 23, the connected SuperHyperStar

N S H S : (V, E),

is highlighted and featured. The obtained neutrosophic SuperHyperSet, by the Algorithm in previous result, of the neutrosophic SuperHyperVertices of the connected SuperHyperStar

N S H S : (V, E),

in the SuperHyperModel Figure 23,

\begin{matrix} {{W_{14}, D_{15}, Z_{14}, C_{15}, E_{15}}, \\ {P_{3}, O_{3}, R_{3}, L_{3}, S_{3}}, {P_{2}, T_{2}, S_{2}, R_{2}, O_{2}}, \\ {O_{6}, O_{7}, K_{7}, P_{6}, H_{7}, J_{7}, E_{7}, L_{7}}, \\ {J_{8}, Z_{10}, W_{10}, V_{10}}, {W_{11}, V_{11}, Z_{11}, C_{12}}, \\ {U_{13}, T_{13}, R_{13}, S_{13}}, {H_{13}}, \\ {E_{13}, D_{13}, C_{13}, Z_{12}},} \end{matrix}

is the neutrosophic SuperHyperStable.

Proposition 3.8.

Assume a connected SuperHyperBipartite

N S H B : (V, E) .

Then a neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet of the interior neutrosophic SuperHyperVertices with only all exceptions in the form of interior neutrosophic SuperHyperVertices titled SuperHyperNeighbors. A neutrosophic SuperHyperStable has the number of the neutrosophic cardinality of the first SuperHyperPart multiplies with the neutrosophic cardinality of the second SuperHyperPart.

Proof.

Assume a connected SuperHyperBipartite

N S H B : (V, E) .

N S H G : (V, E) .

The neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices

V ∖ V ∖ {}

V ∖ V ∖ {x, z}

N S H G : (V, E),

V ∖ V ∖ {z} .

Thus the obvious neutrosophic SuperHyperStable,

V ∖ V ∖ {z},

is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable,

V ∖ V ∖ {z},

is a neutrosophic SuperHyperSet,

V ∖ V ∖ {z},

includes only one neutrosophic SuperHyperVertex doesn’t form any kind of pairs are titled SuperHyperNeighbors in a connected neutrosophic SuperHyperGraph

N S H G : (V, E) .

Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices

V ∖ V ∖ {z},

is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that

V (G)

there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. Thus, in a connected SuperHyperBipartite

N S H B : (V, E),

a neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet of the interior neutrosophic SuperHyperVertices with only all exceptions in the form of interior neutrosophic SuperHyperVertices titled SuperHyperNeighbors. A neutrosophic SuperHyperStable has the number of the neutrosophic cardinality of the first SuperHyperPart multiplies with the neutrosophic cardinality of the second SuperHyperPart. □

Example 3.9.

In the Figure 24, the connected SuperHyperBipartite

N S H B : (V, E),

is highlighted and featured. The obtained neutrosophic SuperHyperSet, by the Algorithm in previous result, of the neutrosophic SuperHyperVertices of the connected SuperHyperBipartite

N S H B : (V, E),

in the SuperHyperModel Figure 24,

\begin{matrix} {{C_{4}, D_{4}, E_{4}, H_{4}}, \\ {K_{4}, J_{4}, L_{4}, O_{4}}, {W_{2}, Z_{2}, C_{3}}, {C_{13}, Z_{12}, V_{12}, W_{12}}, \end{matrix}

is the neutrosophic SuperHyperStable.

Proposition 3.10.

Assume a connected SuperHyperMultipartite

N S H M : (V, E) .

Then a neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet of the interior neutrosophic SuperHyperVertices with only one exception in the form of interior neutrosophic SuperHyperVertices from a SuperHyperPart and only one exception in the form of interior neutrosophic SuperHyperVertices from another SuperHyperPart titled “SuperHyperNeighbors”. A neutrosophic SuperHyperStable has the number of all the summation on the neutrosophic cardinality of the all SuperHyperParts form distinct neutrosophic SuperHyperEdges.

Proof.

Assume a connected SuperHyperMultipartite

N S H M : (V, E) .

N S H G : (V, E) .

The neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices

V ∖ V ∖ {}

V ∖ V ∖ {x, z}

N S H G : (V, E),

V ∖ V ∖ {z} .

Thus the obvious neutrosophic SuperHyperStable,

V ∖ V ∖ {z},

is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable,

V ∖ V ∖ {z},

is a neutrosophic SuperHyperSet,

V ∖ V ∖ {z},

includes only one neutrosophic SuperHyperVertex doesn’t form any kind of pairs are titled SuperHyperNeighbors in a connected neutrosophic SuperHyperGraph

N S H G : (V, E) .

Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices

V ∖ V ∖ {z},

is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that

V (G)

there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. Thus, in a connected SuperHyperMultipartite

N S H M : (V, E),

a neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet of the interior neutrosophic SuperHyperVertices with only one exception in the form of interior neutrosophic SuperHyperVertices from a SuperHyperPart and only one exception in the form of interior neutrosophic SuperHyperVertices from another SuperHyperPart titled “SuperHyperNeighbors”. A neutrosophic SuperHyperStable has the number of all the summation on the neutrosophic cardinality of the all SuperHyperParts form distinct neutrosophic SuperHyperEdges. □

Example 3.11.

In the Figure 25, the connected SuperHyperMultipartite

N S H M : (V, E),

is highlighted and featured. The obtained neutrosophic SuperHyperSet, by the Algorithm in previous result, of the neutrosophic SuperHyperVertices of the connected SuperHyperMultipartite

N S H M : (V, E),

\begin{matrix} {{{L_{4}, E_{4}, O_{4}, D_{4}, J_{4}, K_{4}, H_{4}}, \\ {S_{10}, R_{10}, P_{10}}, \\ {Z_{7}, W_{7}}}, \end{matrix}

in the SuperHyperModel Figure 25, is the neutrosophic SuperHyperStable.

Proposition 3.12.

Assume a connected SuperHyperWheel

N S H W : (V, E) .

Then a neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet of the interior neutrosophic SuperHyperVertices, excluding the SuperHyperCenter, with only one exception in the form of interior neutrosophic SuperHyperVertices from same neutrosophic SuperHyperEdge. A neutrosophic SuperHyperStable has the number of all the number of all the neutrosophic SuperHyperEdges have no common SuperHyperNeighbors for a neutrosophic SuperHyperVertex.

Proof.

Assume a connected SuperHyperWheel

N S H W : (V, E) .

N S H G : (V, E) .

The neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices

V ∖ V ∖ {}

V ∖ V ∖ {x, z}

N S H G : (V, E),

V ∖ V ∖ {z} .

Thus the obvious neutrosophic SuperHyperStable,

V ∖ V ∖ {z},

is up. The obvious simple type-neutrosophic SuperHyperSet of the neutrosophic SuperHyperStable,

V ∖ V ∖ {z},

is a neutrosophic SuperHyperSet,

V ∖ V ∖ {z},

includes only one neutrosophic SuperHyperVertex doesn’t form any kind of pairs are titled SuperHyperNeighbors in a connected neutrosophic SuperHyperGraph

N S H G : (V, E) .

Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperVertices

V ∖ V ∖ {z},

is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet S of neutrosophic SuperHyperVertices such that

V (G)

there’s no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. Thus, in a connected SuperHyperWheel

N S H W : (V, E),

a neutrosophic SuperHyperStable is a neutrosophic SuperHyperSet of the interior neutrosophic SuperHyperVertices, excluding the SuperHyperCenter, with only one exception in the form of interior neutrosophic SuperHyperVertices from same neutrosophic SuperHyperEdge. A neutrosophic SuperHyperStable has the number of all the number of all the neutrosophic SuperHyperEdges have no common SuperHyperNeighbors for a neutrosophic SuperHyperVertex. □

Example 3.13.

In the Figure 26, the connected SuperHyperWheel

N S H W : (V, E),

is highlighted and featured. The obtained neutrosophic SuperHyperSet, by the Algorithm in previous result, of the neutrosophic SuperHyperVertices of the connected SuperHyperWheel

N S H W : (V, E),

\begin{matrix} {V_{5}, \\ {Z_{13}, W_{13}, U_{13}, V_{13}, O_{14}}, \\ {T_{10}, K_{10}, J_{10}}, \\ {E_{7}, C_{7}, Z_{6}}, \\ {T_{14}, U_{14}, R_{15}, S_{15}}}, \end{matrix}

in the SuperHyperModel Figure 26, is the neutrosophic SuperHyperStable.

References

Henry Garrett, “Properties of SuperHyperGraph and Neutrosophic SuperHyperGraph”, Neutrosophic Sets and Systems 49 (2022) 531-561 (doi: 10.5281/zenodo.6456413). (http://fs.unm.edu/NSS/NeutrosophicSuperHyperGraph34.pdf). (https://digitalrepository.unm.edu/ nss_journal/vol49/iss1/34).
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Figure 21. A SuperHyperPath Associated to the Notions of neutrosophic SuperHyperStable in the Example 3.3.

Figure 22. A SuperHyperCycle Associated to the Notions of neutrosophic SuperHyperStable in the Example 3.5.

Figure 23. A SuperHyperStar Associated to the Notions of neutrosophic SuperHyperStable in the Example 3.7.

Figure 24. A SuperHyperBipartite Associated to the Notions of neutrosophic SuperHyperStable in the Example 3.9.

Figure 25. A SuperHyperMultipartite Associated to the Notions of neutrosophic SuperHyperStable in the Example 3.11.

Figure 26. A SuperHyperWheel Associated to the Notions of neutrosophic SuperHyperStable in the Example 3.13.

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